Invited Review
The impact of controllable production rates on the performance of inventory systems: A systematic review of the literature

https://doi.org/10.1016/j.ejor.2020.05.033Get rights and content

Highlights

  • Presents a systematic review of inventory models with controllable production rates.

  • Develops a conceptual framework to facilitate structuring research.

  • Classifies and discusses the sampled works in light of the conceptual framework.

  • Controlling production rates may lower cost and make the system more robust against stockouts.

  • Only a few works considered flexible control and inventory systems with a complex structure.

Abstract

The lot sizing problem has attracted the attention of researchers for more than a century, and it still belongs to the most relevant decision problems in many manufacturing companies. During the evolution of research on lot sizing, the seminal economic order quantity (EOQ) model proposed by Harris [1913. How many parts to make at once. Factory, the Magazine of Management, 10 (2), 135-136.] has remained the most popular model, despite its limitations. To support lot sizing decisions in practice, researchers have frequently extended Harris’ basic EOQ model to better reflect the characteristics of real production processes. One of these extensions is the consideration of controllable (variable) production rates, which gives production planners more flexibility in managing the build-up and depletion of inventory and in controlling costs.

The aim of this paper is to provide a comprehensive and systematic overview of EPQ-type lot sizing models that consider controllable production rates. First, the paper proposes a conceptual framework that captures the characteristics of controllable production rates including the planning horizon (short vs. long term), the number of potential interventions per production run (one vs. multiple), the effect of controllable production rates on the performance of the inventory system (e.g., unit production costs, energy consumption, product quality), and the type of lot sizing model considered (e.g., two-stage models, multi-stage models, multi-item models). Secondly, the paper presents the results of a systematic literature review and evaluates the state-of-research of lot sizing models with controllable production rates. Based on the analysis of the literature, key trends are summarized and promising research opportunities are discussed.

Introduction

The management of inventories is a key determinant of business success in many companies. According to the U.S. Census Bureau (2018), manufacturing companies in the United States held inventories exceeding a total value of US-$ 670 bn on stock in July 2018, which illustrates the enormous potential a reduction of inventories may have also on a national economic level. To support the control of inventories, researchers have developed various stock control methods in the past that mainly focus on determining optimal production and order quantities, an optimal timing of inventory replenishments as well as adequate safety stock levels.

The characteristics of the equipment used for producing a product obviously play an important role in managing the product's inventory levels. In economic production quantity (EPQ) models, machine characteristics are usually reflected, among others, in setup times and costs, production rates and several constraints that govern the build-up and depletion of inventories (e.g., on the point in time when the first shipment can be made from a lot). Many machine characteristics are not fixed in practice, but subject to management control, such as setup times and cost that may depend on production sequences, for example, or production rates that can often be varied within given limits. The work at hand focuses on the latter processing attribute.

To speed up or slow down the build-up of inventories, for example in response to changes in customer demand, production planners often have several options for controlling the production rate in practice. Examples include the adding of workers to a production line, the use of overtime, providing training, modernizing equipment, adding machines, or directly increasing the clock speed of the machine if such an intervention is technically possible (Chen and Munson, 2004). These adjustments can have a short-term (e.g., varying the clock rate) or long-term (e.g., investing in new equipment) character. Despite speeding up or slowing down the build-up of inventories, varying production rates may impact different types of performance measures, such as setup costs, unit production costs, energy costs, product quality-related costs, or CO2 emissions (e.g., Khouja and Mehrez 1994; Giri et al. 2005; Glock 2010; Zanoni et al. 2014a). An eventual adjustment of the production rate therefore carefully needs to take account of the performance measures affected by the adjustment, which need to be adequately reflected in decision support models for stock control.

The aim of this paper is to provide a comprehensive and systematic overview of EPQ-type lot sizing models that consider controllable production rates. The paper first proposes a conceptual framework that captures the characteristics of controllable production rates, such as the planning horizon (e.g., short/long term), available control options (e.g., one variation per production run vs. many), the impact of these adjustments on performance measures (e.g., unit production costs, energy consumption, product quality), and the type of lot sizing model (e.g., two-stage models, multi-stage models, multi-item models) considered. The paper then presents the results of a systematic literature review on the state-of-research of lot sizing models with controllable production rates. Based on the analysis of the literature, key trends are summarized and promising research opportunities are discussed.

The remainder of the paper is structured as follows: The next section discusses typical characteristics of lot sizing models and possible effects of controllable production rates on the lot sizing problem. Based on these characteristics, a framework is developed that is used to categorize the literature. Section 3 describes the systematic literature search and selection strategy. Works that developed lot sizing models with controllable production rates are reviewed in Section 4. In Section 5, main insights of the review are summarized and promising research opportunities are discussed. The paper concludes in Section 6.

Section snippets

The Economic Production Quantity (EPQ) model

Ford Whitman Harris (1913) is credited to be the first author to propose a formal model for optimizing lot sizes (Erlenkotter, 1989; 1990). Harris assumed an infinite replenishment rate in his model and thus neglected the influence of production on the build-up of inventory. This assumption was later relaxed by Taft (1918), who accounted for a finite production rate in his model that later became known as the EPQ model.

The EPQ model determines a production quantity Q that minimizes the sum of

Systematic literature review methodology

The aim of literature reviews, in general, is to synthesize research results, to point out popular streams of research, to assess the knowledge base in a certain research field, and to identify research opportunities (Hochrein and Glock 2012). Systematic literature reviews, which are becoming more and more popular in academic research, rely on a rigorous, robust, clearly-defined and reliable literature search and selection methodology that enables the reader to reproduce sample generation and

Descriptive results

The database search (all numbers effective 31/12/2018) led to 119 initial hits in Scopus and 44 in Business Source Premier. After a first screening for relevance in light of the defined selection criteria and after eliminating duplicate papers that were found in both databases, 145 papers remained in the initial sample, which were complemented by 60 additional works from the snowball search, resulting in a working sample of 205 papers. Papers contained in the working sample were completely read

Data analysis

This section descriptively evaluates the literature sample in light of major model characteristics discussed in Section 4. Some of the results presented here are used to identify research opportunities in Section 5.2. A complete categorization of the sample is provided as an online supplement.

Fig. 5 shows that most of the sampled papers (63) studied two-stage inventory models, followed by 42 multi-product (out of which 37 investigated the ELSP) and 29 supply chain inventory models. Multi-stage

Conclusion

This paper presented the results of a systematic literature review on inventory models with controllable production rates. The objective was to synthesize works in this area, to highlight possible influences of variations in the production rate on the performance of the inventory system, and to identify future research opportunities. A conceptual framework was proposed in addition that considers the main characteristics of lot sizing models with controllable production rates.

In total, 131

Acknowledgments

The authors are grateful to the editor and the anonymous reviewers for their constructive comments that helped to improve an earlier version of this paper substantially.

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